Essential representations of real reductive groups

Abstract: The tempered dual of a real reductive group G equipped with the Fell topology identifies with the space of irreducible representations of the reduced C*-algebra of G. The Connes-Kasparov isomorphism allows to compute the K-theory of this C*-algebra by using the index theory of Dirac-type operators on the symmetric space G/K. The goal of the work presented here (joint with N. Higson, Y. Song and X. Tang) is to provide a representation-theoretic approach to this isomorphism. We will describe the structure of the reduced C*-algebra up to Morita equivalence and characterize representations that contribute to the K-theory in terms of Dirac cohomology.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( video )

Noncommutative Geometry in NYC

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